Further, it is of importance to go back to the actual old field of work in which the geometric conceptions which grew up in the minds of the men of ancient time—conceptions which we are now utilizing and extending—were gradually elaborated. To do this, there is no better way than to dwell very briefly on the work actually done by the old astronomers. * * * * * This programme, then, being agreed to, the first point is to trace the progress of astronomical instruments down to the time of Copernicus and Galileo. During all this period the most generally received doctrine was, that the earth was the centre of the visible heavens; and although there were many variations of this, still the arrangement of Ptolemy, Fig. 1, is a good type of the ideas of the ancients. [Illustration: FIG. 1.—The Heavens according to Ptolemy. ] We begin with man’s first feeble efforts, the work which man was enabled to do by his unaided eye; and we end with the tremendous addition which he got to his observing powers by the invention of the telescope. The first instrument used for astronomical observations was none of man’s making. In the old time the only instrument was the horizon; and, truth to tell, in a land of extended plains and isolated hills, it was not a bad one. Hence it was, doubtless, that observations in the first instance were limited to certain occurrences such as the risings and settings of the stars and the relative apparent distances of the heavenly bodies from each other. So far as we are able to learn from ancient authors, the observations next added were those of the conjunctions of the planets and of eclipses. The Egyptians are stated to have recorded 373 solar, and 832 lunar eclipses; and this statement is probably correct, as the proportions are exact, and there should be the above number of each in from 1,200 to 1,300 years. The Chinese also record an observation, made between the years 2514 and 2436 B.C., of five planets being in conjunction. The Chaldeans appear to have observed the motions of the moon, and an observation in 2227 B.C. is recorded; but these old dates are probably fictitious. It is impossible to regard without surprise the general attention given to astronomical investigation in those early days compared with what we find now. Yet if we attempt to build up for ourselves any idea as to the problems of which the ancients attempted the solution, it is difficult if not impossible to do it; we cannot realize the blank which the heavens presented to them, so many great men have lived between their time and our own, by whose labours we, even if unconsciously, have profited. The first idea seems to have been to observe which stars were rising or setting at seed or harvest time, to divide the heavens into Moon Stations, and then to mark astronomically their monthly and yearly festivals.